The enraged father of a 2-year-old Yonkers girl pumped nine bullets into a paroled sex offender, killing him, because he thought the man had sexually assaulted the child, cops said yesterday.

But an investigation revealed that while Richard Tunley had engaged in “inappropriate conduct,” he had not actually assaulted the girl, cops said.

Tunley, 50, a Vietnam vet who has 15 arrests on his rap sheet, was paroled in April 2001 after serving 2½ years for raping a 13-year-old girl.

The incident began at 2:30 a.m. Monday while Tunley was baby-sitting for the child, the daughter of one of his sisters.

Yonkers Police Commissioner Robert Taggart said the girl’s father, Joshua Torres, 24, returned home and interrupted Tunley during the inappropriate act, which he did not explain.

While a medical exam revealed the girl hadn’t been sexually assaulted, “it is very likely that he was preparing to assault the child,” the commissioner said.

Torres, who has a history of violent criminal acts, beat the stuffing out of Tunley, then let him leave the apartment, police said.

But once the sex offender left, Torres had second thoughts and decided to go after him, police said.

He and four other people drove to Tunley’s sister, Leandra DeGree, who told them her brother, a recovering crack addict, often bought drugs on Riverdale Avenue.

A half-hour later, the posse found Tunley walking along the street. Torres got out of a car and riddled his body with nine bullets – hitting him in the head, chest, arms and legs, Taggart said.

Tunley was pronounced dead at the scene.

DeGree told The Post Torres overreacted.

While Tunley was baby-sitting, “the girl wet her pants and developed a rash and he was applying Vaseline to the rash,” she said. “He went to wipe her down and Torres walked in and took it out of proportion.”

DeGree said that before her brother was shot, he called her to say, “They’re chasing me. They beat me up. I didn’t do anything.

“He didn’t get what he deserved,” she said. “He didn’t need to get gunned down in the street.”

Taggart said Torres called Yonkers police twice to say he was going to surrender, but never showed up. He was still on the loose last night.